Meromorphic Parabolic Starlike Functions Associated with q-Hypergeometric Series

Abstract

We introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk Δ * := { ∈ C : 0 < | | < 1} involving the -hypergeometric functions. We obtained coefficient inequalities, growth and distortion inequalities, and closure results for functions ∈ M ( , , ). We further established some results concerning convolution and the partial sums.

Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator

“…In fact, the theory of univalent functions can be described by using the theory of the q-calculus. Moreover, in recent years, such q-calculus operators as the fractional q-integral and fractional q-derivative operators were used to construct several subclasses of analytic functions (see, for example, [1], [6], [26], [27], [33], [35], [36], [37] and [38]). In particular, Purohit and Raina [36] investigated applications of fractional q-calculus operators to define several classes of functions which are analytic in the open unit disk U.…”

Formula for meromorphic symmetric differences operator with application in the theory of subordination inequality

“…This concept is used to define classes of analytic functions, which are called Ma-Minda type classes [8] . In 2000, Polatoglu and Bolcal [9] furnished the boundaries of the radius of α -convexity for definite relations of analytic functions in U utilizing subordination concept and the authors in [10] achieved adequate conditions for functions being starlike of order α . Similarly, Baner [7] considered the geometric relations in the superior half plane and showing that they have parametric illustration utilizing subordination idea.…”

Certain Subclasses of Univalent Functions Linked with q-Chebyshev Polynomial

“…In reality, the q-calculus theory can be used to describe univalent function theory. Furthermore, in recent years, fractional q-derivative operators and q-integral have been employed to create numerous subclasses of holomorphic functions using q-calculus operators (see for more details [3][4][5][6][7][8][9][10][11]). Purohit and Raina [9] looked at the usage of q-calculus fractional operators to define several holomorphic functions in U.…”